a(n) = Floor[1/2((1-2/Sqrt[3])^n+(1-2/Sqrt[3])^n)].

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =10a(5) =23a(6) =50a(7) =107a(8) =232a(9) =500a(10) =1078a(11) =2323a(12) =5007a(13) =10789a(14) =23248a(15) =50092a(16) =107934a(17) =232566a(18) =501111a(19) =1079745a(20) =2326528a(21) =5012972a(22) =10801454a(23) =23273900a(24) =50148285a(25) =108054537